Modern web applications are increasingly produced through AI-assisted development and rapid no-code deployment pipelines, widening the gap between accelerating software velocity and the limited adaptability of existing security tooling. Pattern-driven scanners fail to reason about novel contexts, while emerging LLM-based penetration testers rely on unconstrained exploration, yielding high cost, unstable behavior, and poor reproducibility. We introduce AWE, a memory-augmented multi-agent framework for autonomous web penetration testing that embeds structured, vulnerability-specific analysis pipelines within a lightweight LLM orchestration layer. Unlike general-purpose agents, AWE couples context aware payload mutations and generations with persistent memory and browser-backed verification to produce deterministic, exploitation-driven results. Evaluated on the 104-challenge XBOW benchmark, AWE achieves substantial gains on injection-class vulnerabilities - 87% XSS success (+30.5% over MAPTA) and 66.7% blind SQL injection success (+33.3%) - while being much faster, cheaper, and more token-efficient than MAPTA, despite using a midtier model (Claude Sonnet 4) versus MAPTA's GPT-5. MAPTA retains higher overall coverage due to broader exploratory capabilities, underscoring the complementary strengths of specialized and general-purpose architectures. Our results demonstrate that architecture matters as much as model reasoning capabilities: integrating LLMs into principled, vulnerability-aware pipelines yields substantial gains in accuracy, efficiency, and determinism for injection-class exploits. The source code for AWE is available at: https://github.com/stuxlabs/AWE